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Three qubits can be entangled in two inequivalent ways
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single
Efficient classical simulation of slightly entangled quantum computations.
  • G. Vidal
  • Computer Science, Physics
    Physical review letters
  • 15 January 2003
TLDR
The results imply that a necessary condition for an exponential computational speedup is that the amount of entanglement increases with the size n of the computation, and provide an explicit lower bound on the required growth.
Computable measure of entanglement
TLDR
A measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system is presented and it is shown that it does not increase under local manipulations of the system.
Efficient simulation of one-dimensional quantum many-body systems.
  • G. Vidal
  • Physics
    Physical review letters
  • 14 October 2003
TLDR
Numerical analysis indicates that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics in sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems.
Entanglement renormalization.
  • G. Vidal
  • Physics
    Physical review letters
  • 8 December 2005
TLDR
Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations, and calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales.
Class of quantum many-body states that can be efficiently simulated.
  • G. Vidal
  • Physics
    Physical review letters
  • 12 October 2006
We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a D-dimensional lattice that can be efficiently simulated with a classical computer, in that
Entanglement in quantum critical phenomena.
TLDR
The results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories.
Classical simulation of quantum many-body systems with a tree tensor network
We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an
Robustness of entanglement
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is
Algorithms for entanglement renormalization
We describe an iterative method to optimize the multiscale entanglement renormalization ansatz for the low-energy subspace of local Hamiltonians on a D -dimensional lattice. For translation-invariant
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